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Some Subfields of Qp, and their Non-Standard Analogues

Published online by Cambridge University Press:  20 November 2018

Diana L. Dubrovsky
Diana L. Dubrovsky*
Affiliation:
Université de Montréal, Montréal, Québec
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The desire to study constructive properties of given mathematical structures goes back many years; we can perhaps mention L. Kronecker and B. L. van der Waerden, two pioneers in this field. With the development of recursion theory it was possible to make precise the notion of "effectively carrying out" the operations in a given algebraic structure. Thus, A. Frölich and J. C. Shepherdson [7] and M. O . Rabin [13] studied computable algebraic structures, i.e. structures whose operations can be viewed as recursive number theoretic relations. A. Robinson [18] and E. W. Madison [11] used the concepts of computable and arithmetically definable structures in order to establish the existence of what can be called non-standard analogues (in a sense that will be specified later) of certain subfields of R and C, the standard models for the theories of real closed and algebraically closed fields respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 473 - 491
Copyright
Copyright © Canadian Mathematical Society 1974

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